Leo-III---1.8.0.UNS-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV954-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 09:01:06 AM UTC 2026

% Result   : Unsatisfiable 18.60s 5.52s
% Output   : Refutation 21.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  383
% Syntax   : Number of formulae    :  767 ( 313 unt;   0 typ;   0 def)
%            Number of atoms       : 1442 ( 449 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives : 46425 ( 848   ~; 675   |;   0   &;44902   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   34 (  14 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   94 (  92 usr;  23 con; 0-7 aty)
%            Number of variables   : 4310 (   0   ^;4310   !;   0   ?;4310   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v_thesis_____decl,type,
    v_thesis____: $o ).

thf(c_WellTypeRT_OWTrt_decl,type,
    c_WellTypeRT_OWTrt: $i > $i > $i > $i > $i > $o ).

thf(v_P_decl,type,
    v_P: $i ).

thf(v_ha_____decl,type,
    v_ha____: $i ).

thf(v_E_____decl,type,
    v_E____: $i ).

thf(v_e_092_060_094isub_0622_____decl,type,
    v_e_092_060_094isub_0622____: $i ).

thf(c_Expr_Oexp_OFAcc_decl,type,
    c_Expr_Oexp_OFAcc: $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_OCond_decl,type,
    c_Expr_Oexp_OCond: $i > $i > $i > $i > $i ).

thf(hAPP_decl,type,
    hAPP: $i > $i > $i ).

thf(c_Map_Omap__add_decl,type,
    c_Map_Omap__add: $i > $i > $i > $i > $i ).

thf(c_in_decl,type,
    c_in: $i > $i > $i > $o ).

thf(c_Map_Odom_decl,type,
    c_Map_Odom: $i > $i > $i > $i ).

thf(hBOOL_decl,type,
    hBOOL: $i > $o ).

thf(c_lessequals_decl,type,
    c_lessequals: $i > $i > $i > $o ).

thf(tc_fun_decl,type,
    tc_fun: $i > $i > $i ).

thf(tc_bool_decl,type,
    tc_bool: $i ).

thf(c_Transitive__Closure_Ortrancl_decl,type,
    c_Transitive__Closure_Ortrancl: $i > $i > $i ).

thf(c_Expr_Oexp_OTryCatch_decl,type,
    c_Expr_Oexp_OTryCatch: $i > $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_OFAss_decl,type,
    c_Expr_Oexp_OFAss: $i > $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_OBinOp_decl,type,
    c_Expr_Oexp_OBinOp: $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_OLAss_decl,type,
    c_Expr_Oexp_OLAss: $i > $i > $i > $i ).

thf(c_TypeRel_Osees__field_decl,type,
    c_TypeRel_Osees__field: $i > $i > $i > $i > $i > $i > $o ).

thf(c_Expr_Oexp_OCall_decl,type,
    c_Expr_Oexp_OCall: $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_OVal_decl,type,
    c_Expr_Oexp_OVal: $i > $i > $i ).

thf(c_Expr_Oexp_Othrow_decl,type,
    c_Expr_Oexp_Othrow: $i > $i > $i ).

thf(c_Expr_Oexp_OCast_decl,type,
    c_Expr_Oexp_OCast: $i > $i > $i > $i ).

thf(c_BigStep_Oeval_decl,type,
    c_BigStep_Oeval: $i > $i > $i > $i > $i > $o ).

thf(tc_List_Olist_decl,type,
    tc_List_Olist: $i > $i ).

thf(tc_String_Ochar_decl,type,
    tc_String_Ochar: $i ).

thf(c_Expr_Oexp_OSeq_decl,type,
    c_Expr_Oexp_OSeq: $i > $i > $i > $i ).

thf(c_Relation_Orefl__on_decl,type,
    c_Relation_Orefl__on: $i > $i > $i > $o ).

thf(c_Relation_OId__on_decl,type,
    c_Relation_OId__on: $i > $i > $i ).

thf(c_Equiv__Relations_Oequiv_decl,type,
    c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).

thf(c_Map_Omap__le_decl,type,
    c_Map_Omap__le: $i > $i > $i > $i > $o ).

thf(class_HOL_Oord_decl,type,
    class_HOL_Oord: $i > $o ).

thf(class_Orderings_Olinorder_decl,type,
    class_Orderings_Olinorder: $i > $o ).

thf(c_Relation_ORange_decl,type,
    c_Relation_ORange: $i > $i > $i > $i ).

thf(c_Relation_ODomain_decl,type,
    c_Relation_ODomain: $i > $i > $i > $i ).

thf(c_Pair_decl,type,
    c_Pair: $i > $i > $i > $i > $i ).

thf(tc_prod_decl,type,
    tc_prod: $i > $i > $i ).

thf(c_Wellfounded_Olex__prod_decl,type,
    c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).

thf(c_Type_Oty_OVoid_decl,type,
    c_Type_Oty_OVoid: $i ).

thf(c_Progress_OWTrt_H_decl,type,
    c_Progress_OWTrt_H: $i > $i > $i > $i > $i > $o ).

thf(c_Type_Oty_ONT_decl,type,
    c_Type_Oty_ONT: $i ).

thf(c_Type_Oty_OClass_decl,type,
    c_Type_Oty_OClass: $i > $i ).

thf(v_sko__TypeRel__Xwiden__Xcases__2_decl,type,
    v_sko__TypeRel__Xwiden__Xcases__2: $i > $i > $i > $i ).

thf(c_TypeRel_Owiden_decl,type,
    c_TypeRel_Owiden: $i > $i > $i > $i > $o ).

thf(t_a_decl,type,
    t_a: $i ).

thf(c_Product__Type_OSigma_decl,type,
    c_Product__Type_OSigma: $i > $i > $i > $i > $i ).

thf(c_Wellfounded_Oacc_decl,type,
    c_Wellfounded_Oacc: $i > $i > $i ).

thf(c_Objects_Ohext_decl,type,
    c_Objects_Ohext: $i > $i > $o ).

thf(tc_nat_decl,type,
    tc_nat: $i ).

thf(tc_Option_Ooption_decl,type,
    tc_Option_Ooption: $i > $i ).

thf(tc_Value_Oval_decl,type,
    tc_Value_Oval: $i ).

thf(tc_Expr_Oexp_decl,type,
    tc_Expr_Oexp: $i > $i ).

thf(c_SmallStep_Ored_decl,type,
    c_SmallStep_Ored: $i > $i ).

thf(c_COMBI_decl,type,
    c_COMBI: $i > $i > $i ).

thf(c_WellType_OWT_decl,type,
    c_WellType_OWT: $i > $i > $i > $i > $o ).

thf(v_T_____decl,type,
    v_T____: $i ).

thf(c_WellType_Osko__WellType__XWT__elim__cases__7__1_decl,type,
    c_WellType_Osko__WellType__XWT__elim__cases__7__1: $i > $i > $i > $i > $i > $i > $i ).

thf(c_WellType_Osko__WellType__XWT__elim__cases__8__3_decl,type,
    c_WellType_Osko__WellType__XWT__elim__cases__8__3: $i > $i > $i > $i > $i > $i > $i ).

thf(c_WellType_Osko__WellType__XWT__elim__cases__8__2_decl,type,
    c_WellType_Osko__WellType__XWT__elim__cases__8__2: $i > $i > $i > $i > $i > $i > $i ).

thf(c_WellType_Osko__WellType__XWT__elim__cases__8__1_decl,type,
    c_WellType_Osko__WellType__XWT__elim__cases__8__1: $i > $i > $i > $i > $i > $i > $i ).

thf(tc_Type_Oty_decl,type,
    tc_Type_Oty: $i ).

thf(c_BigStep_Oevals_decl,type,
    c_BigStep_Oevals: $i > $i > $i > $i > $i > $o ).

thf(c_Conform_Olconf_decl,type,
    c_Conform_Olconf: $i > $i > $i > $i > $i > $o ).

thf(c_WellForm_Owf__prog_decl,type,
    c_WellForm_Owf__prog: $i > $i > $i > $o ).

thf(c_WWellForm_Owwf__J__mdecl_decl,type,
    c_WWellForm_Owwf__J__mdecl: $i ).

thf(c_TypeRel_Ohas__field_decl,type,
    c_TypeRel_Ohas__field: $i > $i > $i > $i > $i > $i > $o ).

thf(v_sko__TypeRel__Xwiden__Xcases__1_decl,type,
    v_sko__TypeRel__Xwiden__Xcases__1: $i > $i > $i > $i ).

thf(c_Recdef_Osame__fst_decl,type,
    c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).

thf(c_Relation_Ototal__on_decl,type,
    c_Relation_Ototal__on: $i > $i > $i > $o ).

thf(c_TypeRel_Osko__TypeRel__Xwiden__Class__1__1_decl,type,
    c_TypeRel_Osko__TypeRel__Xwiden__Class__1__1: $i > $i > $i > $i > $i ).

thf(c_Relation_OImage_decl,type,
    c_Relation_OImage: $i > $i > $i > $i > $i ).

thf(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3_decl,type,
    c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2_decl,type,
    c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1_decl,type,
    c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(v_h_Ha_____decl,type,
    v_h_Ha____: $i ).

thf(v_e_Ha_____decl,type,
    v_e_Ha____: $i ).

thf(v_sko__local__XIH__1_decl,type,
    v_sko__local__XIH__1: $i > $i > $i > $i > $i > $i ).

thf(v_ea_____decl,type,
    v_ea____: $i ).

thf(c_TypeSafe__Mirabelle_Osconf_decl,type,
    c_TypeSafe__Mirabelle_Osconf: $i > $i > $i > $o ).

thf(v_la_____decl,type,
    v_la____: $i ).

thf(v_F_____decl,type,
    v_F____: $i ).

thf(v_D_____decl,type,
    v_D____: $i ).

thf(c_State_Ohp_decl,type,
    c_State_Ohp: $i > $i ).

thf(v_sko__local__XFAssRed1__2__1_decl,type,
    v_sko__local__XFAssRed1__2__1: $i > $i > $i > $i > $i > $i ).

thf(v_sko__local__XFAssRed1__Xhyps__2__1_decl,type,
    v_sko__local__XFAssRed1__Xhyps__2__1: $i > $i > $i > $i > $i > $i ).

thf(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1_decl,type,
    c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4_decl,type,
    c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4: $i > $i > $i > $i > $i ).

thf(c_Conform_Ohconf_decl,type,
    c_Conform_Ohconf: $i > $i > $i > $o ).

thf(v_l_Ha_____decl,type,
    v_l_Ha____: $i ).

thf(241,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAssThrow1_0) ).

thf(1036,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(372,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtFAssNT_0) ).

thf(1337,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(298,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ hAPP ) @ hBOOL )
      | ~ ( D @ ( D @ tc_prod ) @ ( A @ ( G @ hAPP ) @ ( D @ ( D @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ tc_prod ) @ tc_prod ) @ ( D @ ( C @ ( G @ ( F @ c_Recdef_Osame__fst ) ) ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__fstI_0) ).

thf(1168,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ hAPP ) @ hBOOL )
      | ~ ( D @ ( D @ tc_prod ) @ ( A @ ( G @ hAPP ) @ ( D @ ( D @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ tc_prod ) @ tc_prod ) @ ( D @ ( C @ ( G @ ( F @ c_Recdef_Osame__fst ) ) ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(159,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__iff_1) ).

thf(846,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(177,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downward_0) ).

thf(893,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(362,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtSeq_0) ).

thf(1315,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(31,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I44_J_0) ).

thf(468,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(199,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( C @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OThrowThrow_0) ).

thf(941,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( C @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(302,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).

thf(1179,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(35,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I80_J_0) ).

thf(479,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(272,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I161_J_0) ).

thf(1105,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(133,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I103_J_0) ).

thf(777,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(61,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(555,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(95,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I188_J_0) ).

thf(666,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(352,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__Xhyps__2__1 ) ) ) ) @ ( v_P @ c_TypeRel_Owiden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssRed1_Ohyps_I2_J_1) ).

thf(1295,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__Xhyps__2__1 ) ) ) ) @ ( v_P @ c_TypeRel_Owiden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(311,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_0) ).

thf(1200,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(50,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_OVal ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_OVal ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Try_0) ).

thf(523,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_OVal ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_OVal ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(227,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OSeqThrow_0) ).

thf(1005,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(118,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Map_Omap__le ) ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Map_Odom ) ) @ ( C @ ( B @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__implies__dom__le_0) ).

thf(730,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Map_Omap__le ) ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Map_Odom ) ) @ ( C @ ( B @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(254,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD1_0) ).

thf(1068,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(340,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( C @ ( E @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( G @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( C @ ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( E @ ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ ( B @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_6) ).

thf(1269,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( C @ ( E @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( G @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( C @ ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( E @ ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ ( B @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(164,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I1_J_0) ).

thf(861,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(168,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) )
       != ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_1) ).

thf(873,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) )
       != ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(312,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I53_J_0) ).

thf(1205,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(170,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CallRedsObj_0) ).

thf(878,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(21,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I46_J_0) ).

thf(440,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(92,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I168_J_0) ).

thf(655,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(45,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I86_J_0) ).

thf(511,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ( ~ ( A @ ( v_e_092_060_094isub_0622____ @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | v_thesis____ ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(385,plain,
    ! [A: $i] :
      ( ~ ( A @ ( v_e_092_060_094isub_0622____ @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | v_thesis____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(1,negated_conjecture,
    ~ v_thesis____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(384,plain,
    ~ v_thesis____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(42,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_2) ).

thf(500,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(112,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( C @ c_BigStep_Oeval ) ) ) ) )
      | ( A
        = ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__cases_I1_J_0) ).

thf(715,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( C @ c_BigStep_Oeval ) ) ) ) )
      | ( A
        = ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(342,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XIH__1 ) ) ) ) @ ( v_e_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IH_0) ).

thf(1275,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XIH__1 ) ) ) ) @ ( v_e_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(323,axiom,
    tc_nat @ class_HOL_Oord,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

thf(1233,plain,
    tc_nat @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(368,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I1_J_0) ).

thf(1327,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(125,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I109_J_0) ).

thf(747,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(201,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).

thf(945,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(381,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E = c_Type_Oty_OVoid )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_1) ).

thf(1354,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E = c_Type_Oty_OVoid )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(318,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).

thf(1222,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(335,axiom,
    ! [A: $i] : ( A @ ( A @ c_Objects_Ohext ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__refl_0) ).

thf(1260,plain,
    ! [A: $i] : ( A @ ( A @ c_Objects_Ohext ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(106,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_OVal ) @ ( C @ c_BigStep_Oeval ) ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__cases_I1_J_1) ).

thf(698,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_OVal ) @ ( C @ c_BigStep_Oeval ) ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(9,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( H @ ( B @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ~ ( G @ ( F @ ( A @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__field__fun_0) ).

thf(404,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( H @ ( B @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ~ ( G @ ( F @ ( A @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(308,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OBinOpThrow2_0) ).

thf(1196,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(14,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = G )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_1) ).

thf(417,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = G )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(212,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OThrowRed_0) ).

thf(973,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(383,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( F @ ( G @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_11) ).

thf(1359,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( F @ ( G @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(338,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BinOp1Reds_0) ).

thf(1265,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(321,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I61_J_0) ).

thf(1228,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(90,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(651,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(327,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CondReds_0) ).

thf(1243,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(280,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OTryRed_0) ).

thf(1127,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(348,axiom,
    ( ( t_a @ ( v_P @ c_COMBI ) )
    = v_P ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).

thf(1287,plain,
    ( ( t_a @ ( v_P @ c_COMBI ) )
    = v_P ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(369,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E = c_Type_Oty_OVoid )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_2) ).

thf(1330,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E = c_Type_Oty_OVoid )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(366,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( F @ ( G @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( E @ ( A @ ( G @ ( C @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_5) ).

thf(1323,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( F @ ( G @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( E @ ( A @ ( G @ ( C @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(307,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = F )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_0) ).

thf(1191,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = F )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(283,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_has__visible__field_0) ).

thf(1132,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(361,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( F @ ( G @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_14) ).

thf(1313,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( F @ ( G @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(344,axiom,
    v_T____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622____ @ ( v_D____ @ ( v_F____ @ ( v_ea____ @ c_Expr_Oexp_OFAss ) ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_0) ).

thf(1279,plain,
    v_T____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622____ @ ( v_D____ @ ( v_F____ @ ( v_ea____ @ c_Expr_Oexp_OFAss ) ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(181,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( F @ ( D @ ( G @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTFAcc_0) ).

thf(902,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( F @ ( D @ ( G @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(264,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SeqReds2_0) ).

thf(1087,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(329,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAcc ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OFAccThrow_0) ).

thf(1247,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAcc ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(364,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtFAccNT_0) ).

thf(1319,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(24,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(448,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(270,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ~ ( D @ ( C @ ( E @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__trans_0) ).

thf(1100,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ~ ( D @ ( C @ ( E @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(86,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(638,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(161,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCondRed_0) ).

thf(853,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(191,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( B @ ( D @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_WellType_Osko__WellType__XWT__elim__cases__8__2 ) ) ) ) ) @ ( D @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_WellType_Osko__WellType__XWT__elim__cases__8__1 ) ) ) ) ) @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I8_J_2) ).

thf(924,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( B @ ( D @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_WellType_Osko__WellType__XWT__elim__cases__8__2 ) ) ) ) ) @ ( D @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_WellType_Osko__WellType__XWT__elim__cases__8__1 ) ) ) ) ) @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(73,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( E @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ c_in ) ) )
      | ( ( B @ ( A @ hAPP ) )
        = ( B @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__def_0) ).

thf(591,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( E @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ c_in ) ) )
      | ( ( B @ ( A @ hAPP ) )
        = ( B @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(22,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I180_J_0) ).

thf(443,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(46,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ ( A @ c_Relation_Orefl__on ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).

thf(514,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ ( A @ c_Relation_Orefl__on ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(197,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt__env__mono_0) ).

thf(937,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(209,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CastReds_0) ).

thf(966,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(356,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( G @ ( F @ ( B @ ( D @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1 ) ) ) ) ) ) @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I7_J_1) ).

thf(1302,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( G @ ( F @ ( B @ ( D @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1 ) ) ) ) ) ) @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(128,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I97_J_0) ).

thf(756,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(37,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I62_J_0) ).

thf(485,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(154,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( F @ ( B @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( D @ ( A @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Objects_Ohext ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__hext__incr_0) ).

thf(834,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( F @ ( B @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( D @ ( A @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Objects_Ohext ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(235,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( E @ ( D @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTSeq_0) ).

thf(1020,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( E @ ( D @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(68,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I70_J_0) ).

thf(574,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(304,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_Relation_Ototal__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) )
      | ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ( B = A )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__def_0) ).

thf(1183,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_Relation_Ototal__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) )
      | ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ( B = A )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(346,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( I @ ( H @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtFAss_0) ).

thf(1283,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( I @ ( H @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(246,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( A @ ( B @ c_Map_Omap__le ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__antisym_0) ).

thf(1051,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( A @ ( B @ c_Map_Omap__le ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(149,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) @ ( D @ ( C @ ( B @ c_Progress_OWTrt_H ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__elim__cases_0) ).

thf(821,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) @ ( D @ ( C @ ( B @ c_Progress_OWTrt_H ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(76,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I68_J_0) ).

thf(602,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(256,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I51_J_0) ).

thf(1072,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(6,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).

thf(396,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(380,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ ( H @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E @ ( C @ ( H @ ( B @ ( G @ ( D @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_9) ).

thf(1351,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ ( H @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E @ ( C @ ( H @ ( B @ ( G @ ( D @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(224,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_Conform_Olconf ) ) ) ) )
      | ~ ( B @ ( F @ c_Objects_Ohext ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Olconf ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lconf__hext_0) ).

thf(998,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_Conform_Olconf ) ) ) ) )
      | ~ ( B @ ( F @ c_Objects_Ohext ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Olconf ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(376,axiom,
    tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( v_P @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_l_Ha____ @ ( v_h_Ha____ @ c_Pair ) ) ) @ ( v_e_Ha____ @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( v_ea____ @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red_0) ).

thf(1345,plain,
    tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( v_P @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_l_Ha____ @ ( v_h_Ha____ @ c_Pair ) ) ) @ ( v_e_Ha____ @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( v_ea____ @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(17,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I189_J_0) ).

thf(428,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(189,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD_0) ).

thf(920,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(200,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I50_J_0) ).

thf(942,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(358,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( B @ c_Expr_Oexp_OCast ) ) @ ( E @ ( D @ ( C @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I6_J_0) ).

thf(1306,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( B @ c_Expr_Oexp_OCast ) ) @ ( E @ ( D @ ( C @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(310,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OBinOpThrow1_0) ).

thf(1199,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(291,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCastRed_0) ).

thf(1153,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(145,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I146_J_0) ).

thf(810,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(58,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I79_J_0) ).

thf(546,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(139,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(793,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(360,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt__wt_H_0) ).

thf(1311,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(54,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I63_J_0) ).

thf(534,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(141,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I107_J_0) ).

thf(798,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(296,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I52_J_0) ).

thf(1163,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(319,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( G @ ( B @ c_Pair ) ) ) @ ( F @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( E @ ( A @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oeval ) ) ) ) )
      | ( B @ ( A @ c_Objects_Ohext ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__hext_0) ).

thf(1223,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( G @ ( B @ c_Pair ) ) ) @ ( F @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( E @ ( A @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oeval ) ) ) ) )
      | ( B @ ( A @ c_Objects_Ohext ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(266,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( B @ ( G @ c_Pair ) ) ) @ ( F @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( A @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oevals ) ) ) ) )
      | ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evals__lcl__incr_0) ).

thf(1091,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( B @ ( G @ c_Pair ) ) ) @ ( F @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( A @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oevals ) ) ) ) )
      | ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(375,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( A @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( C @ ( B @ c_Pair ) ) ) @ ( I @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( F @ ( E @ c_Pair ) ) ) @ ( G @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( H @ ( G @ ( D @ ( E @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( F @ ( E @ ( A @ c_Conform_Olconf ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( C @ ( B @ ( A @ c_Conform_Olconf ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__preserves__lconf_0) ).

thf(1343,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( A @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( C @ ( B @ c_Pair ) ) ) @ ( I @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( F @ ( E @ c_Pair ) ) ) @ ( G @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( H @ ( G @ ( D @ ( E @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( F @ ( E @ ( A @ c_Conform_Olconf ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( C @ ( B @ ( A @ c_Conform_Olconf ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(205,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAssRed1_0) ).

thf(952,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(333,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).

thf(1255,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(278,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ tc_prod ) @ ( D @ ( E @ ( B @ ( F @ c_Product__Type_OSigma ) ) ) @ ( D @ ( E @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD2_0) ).

thf(1123,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ tc_prod ) @ ( D @ ( E @ ( B @ ( F @ c_Product__Type_OSigma ) ) ) @ ( D @ ( E @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(316,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I160_J_0) ).

thf(1217,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(63,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I85_J_0) ).

thf(561,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(147,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I181_J_0) ).

thf(815,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(117,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( A @ c_BigStep_Oeval ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Val_0) ).

thf(729,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( A @ c_BigStep_Oeval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(326,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_1) ).

thf(1238,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(407,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(104,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I156_J_0) ).

thf(693,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(187,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SeqRedsThrow_0) ).

thf(916,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(65,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ c_in ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( E @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I3_J_0) ).

thf(566,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ c_in ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( E @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(101,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I152_J_0) ).

thf(682,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(157,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CastRedsThrow_0) ).

thf(842,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(231,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAccReds_0) ).

thf(1012,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(71,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_2) ).

thf(583,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(152,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaI_0) ).

thf(830,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(294,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCallObj_0) ).

thf(1159,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(28,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OThrowThrow_0) ).

thf(461,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(259,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( B @ ( A @ c_TypeRel_Owiden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__refl_0) ).

thf(1079,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( B @ ( A @ c_TypeRel_Owiden ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(237,axiom,
    c_Type_Oty_OVoid != c_Type_Oty_ONT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I6_J_0) ).

thf(1027,plain,
    c_Type_Oty_OVoid != c_Type_Oty_ONT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(350,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_0) ).

thf(1291,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(110,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I167_J_0) ).

thf(710,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(123,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I216_J_0) ).

thf(742,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(203,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LAssRedsThrow_0) ).

thf(948,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(252,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( I @ ( H @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I10_J_0) ).

thf(1064,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( I @ ( H @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(214,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I137_J_0) ).

thf(980,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(268,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__def_1) ).

thf(1096,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(228,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( D @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SeqReds_0) ).

thf(1006,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( D @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(3,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I162_J_0) ).

thf(388,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(166,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_1) ).

thf(869,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(135,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I176_J_0) ).

thf(783,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(219,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__le__mapE_0) ).

thf(989,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(265,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BinOp2Reds_0) ).

thf(1089,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(324,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAccRedsThrow_0) ).

thf(1234,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(32,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(471,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(173,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( I @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( H @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BinOpRedsThrow2_0) ).

thf(884,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( I @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( H @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(261,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).

thf(1082,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(38,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I206_J_0) ).

thf(488,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(195,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(933,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(127,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I186_J_0) ).

thf(753,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(55,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I57_J_0) ).

thf(537,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(96,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I187_J_0) ).

thf(669,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(233,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( E @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( E @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ThrowRedsThrow_0) ).

thf(1016,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( E @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( E @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(292,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( E @ ( B @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__le ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__le__mapI_0) ).

thf(1155,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( E @ ( B @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__le ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(257,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAssRed2_0) ).

thf(1075,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(34,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I106_J_0) ).

thf(476,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(100,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I211_J_0) ).

thf(679,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(243,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_2) ).

thf(1039,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(107,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I224_J_0) ).

thf(701,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(353,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( B @ ( D @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I7_J_0) ).

thf(1297,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( B @ ( D @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(322,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_2) ).

thf(1231,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(282,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedSeq_0) ).

thf(1131,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(250,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( E @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( E @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ThrowReds_0) ).

thf(1060,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( E @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( E @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(114,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ORange ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).

thf(721,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ORange ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(66,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I195_J_0) ).

thf(569,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(77,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I218_J_0) ).

thf(605,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(337,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD2_0) ).

thf(1263,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(223,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAccThrow_0) ).

thf(997,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(47,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OCall ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CallObjThrow_0) ).

thf(515,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OCall ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(290,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OCast ) ) @ ( D @ ( C @ c_WellType_OWT ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I6_J_0) ).

thf(1150,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OCast ) ) @ ( D @ ( C @ c_WellType_OWT ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(330,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).

thf(1249,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(216,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Objects_Ohext ) )
      | ~ ( B @ ( C @ c_Objects_Ohext ) )
      | ( B @ ( A @ c_Objects_Ohext ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__trans_0) ).

thf(984,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Objects_Ohext ) )
      | ~ ( B @ ( C @ c_Objects_Ohext ) )
      | ( B @ ( A @ c_Objects_Ohext ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(185,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I54_J_0) ).

thf(911,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(370,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E @ ( B @ ( D @ ( A @ ( G @ ( C @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_10) ).

thf(1333,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E @ ( B @ ( D @ ( A @ ( G @ ( C @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(263,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OLAssThrow_0) ).

thf(1086,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(44,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I67_J_0) ).

thf(508,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(247,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OBinOpRed2_0) ).

thf(1054,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(299,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_0) ).

thf(1170,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(62,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I75_J_0) ).

thf(558,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(192,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I175_J_0) ).

thf(926,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(7,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I183_J_0) ).

thf(398,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(240,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCastThrow_0) ).

thf(1035,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(113,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I92_J_0) ).

thf(718,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(175,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OLAssRed_0) ).

thf(888,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(12,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( D @ ( C @ ( F @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__field__idemp_0) ).

thf(412,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( D @ ( C @ ( F @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(126,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I225_J_0) ).

thf(750,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(16,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I98_J_0) ).

thf(425,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(288,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssReds1_0) ).

thf(1146,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(150,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( A @ ( C @ c_TypeRel_Owiden ) ) ) )
      | ( B = A )
      | ( B
        = ( B @ ( A @ ( C @ v_sko__TypeRel__Xwiden__Xcases__2 ) ) @ c_Type_Oty_OClass ) )
      | ( A = c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen_Ocases_2) ).

thf(824,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( A @ ( C @ c_TypeRel_Owiden ) ) ) )
      | ( B = A )
      | ( B
        = ( B @ ( A @ ( C @ v_sko__TypeRel__Xwiden__Xcases__2 ) ) @ c_Type_Oty_OClass ) )
      | ( A = c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(124,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(745,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(119,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I102_J_0) ).

thf(732,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(279,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTThrow_0) ).

thf(1125,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(132,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_1) ).

thf(772,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(69,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I177_J_0) ).

thf(577,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(182,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I154_J_0) ).

thf(904,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(213,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Type_Oty_OClass )
       != ( B @ c_Type_Oty_OClass ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Oinject_0) ).

thf(975,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Type_Oty_OClass )
       != ( B @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).

thf(572,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(111,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(713,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(249,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( G @ ( F @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( D @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( C @ c_Map_Omap__add ) ) ) @ ( F @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ c_Map_Omap__add ) ) ) @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Red__lcl__add_0) ).

thf(1058,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( G @ ( F @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( D @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( C @ c_Map_Omap__add ) ) ) @ ( F @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ c_Map_Omap__add ) ) ) @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(30,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( I @ ( tc_String_Ochar @ tc_List_Olist @ ( J @ c_Expr_Oexp_OVal ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( I @ ( E @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OFAssThrow2_0) ).

thf(466,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( I @ ( tc_String_Ochar @ tc_List_Olist @ ( J @ c_Expr_Oexp_OVal ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( I @ ( E @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(143,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I207_J_0) ).

thf(804,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(108,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( B @ ( H @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ~ ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__field__fun_1) ).

thf(704,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( B @ ( H @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ~ ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(202,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ c_Type_Oty_OClass @ ( c_Type_Oty_ONT @ ( A @ c_TypeRel_Owiden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__Class_2) ).

thf(947,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ c_Type_Oty_OClass @ ( c_Type_Oty_ONT @ ( A @ c_TypeRel_Owiden ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(56,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I212_J_0) ).

thf(540,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(97,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(672,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(4,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ c_in ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( E @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I1_J_0) ).

thf(391,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ c_in ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( E @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(285,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I11_J_0) ).

thf(1139,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(79,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = I )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_3) ).

thf(611,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = I )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(137,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I217_J_0) ).

thf(787,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(130,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_1) ).

thf(764,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(180,axiom,
    v_T____ = c_Type_Oty_OVoid,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_void_0) ).

thf(900,plain,
    v_T____ = c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(276,axiom,
    c_Type_Oty_ONT != c_Type_Oty_OVoid,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I7_J_0) ).

thf(1117,plain,
    c_Type_Oty_ONT != c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(230,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCallThrowObj_0) ).

thf(1011,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(379,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( v_e_092_060_094isub_0622____ @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | v_thesis____ ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).

thf(1349,plain,
    ! [A: $i] :
      ( ~ ( A @ ( v_e_092_060_094isub_0622____ @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | v_thesis____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(287,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( G @ ( D @ ( D @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ tc_prod ) @ tc_prod ) @ ( D @ ( C @ ( G @ ( F @ c_Wellfounded_Olex__prod ) ) ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__lex__prod_3) ).

thf(1144,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( G @ ( D @ ( D @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ tc_prod ) @ tc_prod ) @ ( D @ ( C @ ( G @ ( F @ c_Wellfounded_Olex__prod ) ) ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(121,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I45_J_0) ).

thf(737,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(80,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_1) ).

thf(616,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(75,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I151_J_0) ).

thf(599,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(300,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OCast ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OCastThrow_0) ).

thf(1175,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OCast ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(171,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LAssReds_0) ).

thf(880,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(19,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I192_J_0) ).

thf(434,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(176,axiom,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_ONT ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I21_J_0) ).

thf(890,plain,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_ONT ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(373,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( F @ c_Objects_Ohext ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__hext__mono_0) ).

thf(1339,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( F @ c_Objects_Ohext ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(60,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I169_J_0) ).

thf(552,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(74,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_0) ).

thf(594,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(81,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I87_J_0) ).

thf(621,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(367,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__implies__WTrt_0) ).

thf(1325,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(178,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( D @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OSeqRed_0) ).

thf(895,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( D @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(131,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I77_J_0) ).

thf(769,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(236,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = H )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_2) ).

thf(1022,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = H )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(301,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( I @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( H @ ( D @ ( I @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ~ ( G @ ( F @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( H @ ( G @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTFAss_0) ).

thf(1177,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( I @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( H @ ( D @ ( I @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ~ ( G @ ( F @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( H @ ( G @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(40,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I170_J_0) ).

thf(494,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(260,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( D @ ( E @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( F @ ( C @ ( A @ ( E @ ( B @ ( D @ c_WellType_Osko__WellType__XWT__elim__cases__8__1 ) ) ) ) ) @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I8_J_1) ).

thf(1080,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( D @ ( E @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( F @ ( C @ ( A @ ( E @ ( B @ ( D @ c_WellType_Osko__WellType__XWT__elim__cases__8__1 ) ) ) ) ) @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(160,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = G )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_1) ).

thf(848,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = G )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(49,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I66_J_0) ).

thf(520,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(102,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
       != ( B @ ( C @ c_Expr_Oexp_OVal ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I3_J_0) ).

thf(685,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
       != ( B @ ( C @ c_Expr_Oexp_OVal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(215,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__map__add_0) ).

thf(983,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(207,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CallRedsThrowObj_0) ).

thf(959,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(253,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I5_J_0) ).

thf(1066,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(134,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I93_J_0) ).

thf(780,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(26,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I194_J_0) ).

thf(455,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(78,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(608,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(274,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I8_J_0) ).

thf(1113,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(225,axiom,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_OVoid ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I9_J_0) ).

thf(1000,plain,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_OVoid ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(331,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) )
        = ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_0) ).

thf(1250,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) )
        = ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(271,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( C @ ( A @ ( B @ c_TypeRel_Owiden ) ) ) )
      | ( C = A )
      | ( A
        = ( C @ ( A @ ( B @ v_sko__TypeRel__Xwiden__Xcases__1 ) ) @ c_Type_Oty_OClass ) )
      | ( A = c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen_Ocases_0) ).

thf(1102,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( C @ ( A @ ( B @ c_TypeRel_Owiden ) ) ) )
      | ( C = A )
      | ( A
        = ( C @ ( A @ ( B @ v_sko__TypeRel__Xwiden__Xcases__1 ) ) @ c_Type_Oty_OClass ) )
      | ( A = c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(43,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( E @ c_in ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( E @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I2_J_0) ).

thf(505,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( E @ c_in ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( E @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(18,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I171_J_0) ).

thf(431,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(91,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(653,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(190,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( B @ ( D @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_WellType_Osko__WellType__XWT__elim__cases__8__2 ) ) ) ) ) @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_WellType_Osko__WellType__XWT__elim__cases__8__3 ) ) ) ) ) @ ( A @ c_TypeRel_Owiden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I8_J_4) ).

thf(922,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( B @ ( D @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_WellType_Osko__WellType__XWT__elim__cases__8__2 ) ) ) ) ) @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_WellType_Osko__WellType__XWT__elim__cases__8__3 ) ) ) ) ) @ ( A @ c_TypeRel_Owiden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(93,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
       != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I14_J_0) ).

thf(658,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
       != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(314,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I139_J_0) ).

thf(1213,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(151,axiom,
    ! [A: $i] :
      ( c_Type_Oty_OVoid
     != ( A @ c_Type_Oty_OClass ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I8_J_0) ).

thf(827,plain,
    ! [A: $i] :
      ( c_Type_Oty_OVoid
     != ( A @ c_Type_Oty_OClass ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(244,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_1) ).

thf(1044,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(328,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( G @ ( E @ ( H @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I8_J_0) ).

thf(1245,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( G @ ( E @ ( H @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(5,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(394,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ ( A @ c_Map_Omap__le ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__refl_0) ).

thf(986,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ ( A @ c_Map_Omap__le ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(33,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I101_J_0) ).

thf(473,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(357,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_H__wt_0) ).

thf(1304,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(297,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).

thf(1166,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(313,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

thf(1208,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(53,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I219_J_0) ).

thf(531,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(140,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I84_J_0) ).

thf(795,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(94,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I69_J_0) ).

thf(663,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(343,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XIH__1 ) ) ) ) @ ( v_P @ c_TypeRel_Owiden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IH_1) ).

thf(1277,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XIH__1 ) ) ) ) @ ( v_P @ c_TypeRel_Owiden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(198,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_TryRedsVal_0) ).

thf(939,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(234,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( B @ ( G @ c_Pair ) ) ) @ ( F @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( A @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oeval ) ) ) ) )
      | ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__lcl__incr_0) ).

thf(1018,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( B @ ( G @ c_Pair ) ) ) @ ( F @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( A @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oeval ) ) ) ) )
      | ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(155,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I136_J_0) ).

thf(836,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(245,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( B @ ( F @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( A @ ( D @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__lcl__incr_0) ).

thf(1049,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( B @ ( F @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( A @ ( D @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(284,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_1) ).

thf(1134,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(89,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I78_J_0) ).

thf(648,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(210,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).

thf(968,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(27,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I113_J_0) ).

thf(458,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(303,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).

thf(1181,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(51,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I74_J_0) ).

thf(525,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(226,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
      | ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( A @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ ( G @ ( F @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_extend__eval_0) ).

thf(1003,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
      | ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( A @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ ( G @ ( F @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(103,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I213_J_0) ).

thf(690,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(87,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I114_J_0) ).

thf(640,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(255,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).

thf(1070,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(206,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

thf(954,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(339,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_13) ).

thf(1267,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(11,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I157_J_0) ).

thf(409,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(269,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
      | ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( A @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ ( G @ ( F @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_extend__1__eval_0) ).

thf(1098,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
      | ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( A @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ ( G @ ( F @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(221,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( G @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ tc_prod ) @ tc_prod ) @ ( D @ ( C @ ( H @ ( G @ c_Wellfounded_Olex__prod ) ) ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__lex__prod_2) ).

thf(993,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( G @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ tc_prod ) @ tc_prod ) @ ( D @ ( C @ ( H @ ( G @ c_Wellfounded_Olex__prod ) ) ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(70,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I71_J_0) ).

thf(580,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(162,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_1) ).

thf(855,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(320,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ c_Type_Oty_OClass @ ( A @ ( C @ c_TypeRel_Owiden ) ) ) )
      | ( A = c_Type_Oty_ONT )
      | ( A
        = ( D @ ( A @ ( C @ ( B @ c_TypeRel_Osko__TypeRel__Xwiden__Class__1__1 ) ) ) @ c_Type_Oty_OClass ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__Class_0) ).

thf(1225,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ c_Type_Oty_OClass @ ( A @ ( C @ c_TypeRel_Owiden ) ) ) )
      | ( A = c_Type_Oty_ONT )
      | ( A
        = ( D @ ( A @ ( C @ ( B @ c_TypeRel_Osko__TypeRel__Xwiden__Class__1__1 ) ) ) @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(109,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I56_J_0) ).

thf(707,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(13,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I90_J_0) ).

thf(414,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(211,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RangeI_0) ).

thf(971,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(98,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I99_J_0) ).

thf(673,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(355,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_4) ).

thf(1300,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(305,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I145_J_0) ).

thf(1186,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(29,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I210_J_0) ).

thf(463,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(363,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( G @ ( E @ ( H @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtFAcc_0) ).

thf(1317,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( G @ ( E @ ( H @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(347,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( A @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( G @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( E @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( F @ ( E @ ( B @ ( D @ c_State_Ohp @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( D @ ( B @ ( A @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ( C @ ( B @ ( A @ c_TypeSafe__Mirabelle_Osconf ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__preserves__sconf_0) ).

thf(1285,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( A @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( G @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( E @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( F @ ( E @ ( B @ ( D @ c_State_Ohp @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( D @ ( B @ ( A @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ( C @ ( B @ ( A @ c_TypeSafe__Mirabelle_Osconf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(88,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_2) ).

thf(643,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(317,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ ( F @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD1_0) ).

thf(1220,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ ( F @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(183,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedTry_0) ).

thf(907,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(334,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I144_J_0) ).

thf(1257,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(286,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I60_J_0) ).

thf(1141,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(165,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_0) ).

thf(864,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(229,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I174_J_0) ).

thf(1008,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(446,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(341,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( F @ ( G @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( H @ ( C @ ( E @ ( B @ ( G @ ( D @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( E @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_3) ).

thf(1272,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( F @ ( G @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( H @ ( C @ ( E @ ( B @ ( G @ ( D @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( E @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(220,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OFAssThrow1_0) ).

thf(991,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I150_J_0) ).

thf(497,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(169,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).

thf(876,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(83,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_0) ).

thf(627,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(194,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BinOpRedsThrow1_0) ).

thf(931,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(36,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I100_J_0) ).

thf(482,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(129,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_0) ).

thf(759,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(315,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAssThrow2_0) ).

thf(1216,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(306,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( I @ ( tc_String_Ochar @ tc_List_Olist @ ( J @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( I @ ( D @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssRedsThrow2_0) ).

thf(1189,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( I @ ( tc_String_Ochar @ tc_List_Olist @ ( J @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( I @ ( D @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(273,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = I )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_3) ).

thf(1108,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = I )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(25,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = F )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_0) ).

thf(450,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = F )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(262,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( D @ ( E @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( C @ ( F @ ( A @ ( E @ ( B @ ( D @ c_WellType_Osko__WellType__XWT__elim__cases__8__3 ) ) ) ) ) @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I8_J_3) ).

thf(1084,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( D @ ( E @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( C @ ( F @ ( A @ ( E @ ( B @ ( D @ c_WellType_Osko__WellType__XWT__elim__cases__8__3 ) ) ) ) ) @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(293,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OLAss ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OLAssThrow_0) ).

thf(1157,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OLAss ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(365,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( A @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( I @ ( B @ c_Pair ) ) ) @ ( H @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( G @ ( C @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( F @ ( E @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( C @ ( A @ c_Conform_Ohconf ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Conform_Ohconf ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__preserves__hconf_0) ).

thf(1321,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( A @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( I @ ( B @ c_Pair ) ) ) @ ( H @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( G @ ( C @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( F @ ( E @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( C @ ( A @ c_Conform_Ohconf ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Conform_Ohconf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(349,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__2__1 ) ) ) ) @ ( v_P @ c_TypeRel_Owiden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssRed1_I2_J_1) ).

thf(1289,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__2__1 ) ) ) ) @ ( v_P @ c_TypeRel_Owiden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(158,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_COMBI ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).

thf(844,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_COMBI ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(48,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I140_J_0) ).

thf(517,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(374,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( F @ ( G @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( F @ ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_8) ).

thf(1341,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( F @ ( G @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( F @ ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(251,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ c_Expr_Oexp_OVal ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ~ ( F @ ( E @ ( G @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( F @ ( E @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Seq_0) ).

thf(1062,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ c_Expr_Oexp_OVal ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ~ ( F @ ( E @ ( G @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( F @ ( E @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(84,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I141_J_0) ).

thf(632,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(8,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I96_J_0) ).

thf(401,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(136,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(786,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(222,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( G @ ( B @ c_Pair ) ) ) @ ( F @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( E @ ( A @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oevals ) ) ) ) )
      | ( B @ ( A @ c_Objects_Ohext ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evals__hext_0) ).

thf(995,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( G @ ( B @ c_Pair ) ) ) @ ( F @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( E @ ( A @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oevals ) ) ) ) )
      | ( B @ ( A @ c_Objects_Ohext ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(72,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I115_J_0) ).

thf(588,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(332,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
      | ~ ( D @ ( C @ ( B @ ( A @ ( E @ c_BigStep_Oeval ) ) ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( E @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_big__by__small_0) ).

thf(1253,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
      | ~ ( D @ ( C @ ( B @ ( A @ ( E @ c_BigStep_Oeval ) ) ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( E @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(208,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_0) ).

thf(961,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(146,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ODomain ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).

thf(813,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ODomain ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(238,axiom,
    ! [A: $i] :
      ( c_Type_Oty_ONT
     != ( A @ c_Type_Oty_OClass ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I20_J_0) ).

thf(1030,plain,
    ! [A: $i] :
      ( c_Type_Oty_ONT
     != ( A @ c_Type_Oty_OClass ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(186,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( C @ c_Expr_Oexp_OFAcc ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( C @ ( F @ ( A @ ( E @ ( B @ ( D @ c_WellType_Osko__WellType__XWT__elim__cases__7__1 ) ) ) ) ) @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I7_J_0) ).

thf(914,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( C @ c_Expr_Oexp_OFAcc ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( C @ ( F @ ( A @ ( E @ ( B @ ( D @ c_WellType_Osko__WellType__XWT__elim__cases__7__1 ) ) ) ) ) @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(351,axiom,
    v_T____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622____ @ ( v_D____ @ ( v_F____ @ ( v_ea____ @ c_Expr_Oexp_OFAss ) ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(1294,plain,
    v_T____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622____ @ ( v_D____ @ ( v_F____ @ ( v_ea____ @ c_Expr_Oexp_OFAss ) ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(193,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAccRed_0) ).

thf(929,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(258,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__trans_0) ).

thf(1077,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(153,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downwards_0) ).

thf(832,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(359,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__2__1 ) ) ) ) @ ( v_e_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssRed1_I2_J_0) ).

thf(1309,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__2__1 ) ) ) ) @ ( v_e_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(59,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I112_J_0) ).

thf(549,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(295,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssRedsThrow1_0) ).

thf(1161,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(275,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(1116,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(378,axiom,
    c_Type_Oty_ONT @ ( v_e_Ha____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_calculation_0) ).

thf(1348,plain,
    c_Type_Oty_ONT @ ( v_e_Ha____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(345,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( C @ ( E @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( G @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( B @ c_TypeRel_Owiden ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_12) ).

thf(1280,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( C @ ( E @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( G @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( B @ c_TypeRel_Owiden ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(204,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CondRedsThrow_0) ).

thf(950,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(148,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ tc_prod ) @ ( F @ ( C @ tc_prod ) @ tc_prod ) @ ( F @ ( C @ ( H @ ( D @ c_Wellfounded_Olex__prod ) ) ) @ ( F @ ( C @ tc_prod ) @ ( F @ ( C @ tc_prod ) @ ( F @ ( C @ ( G @ ( B @ c_Pair ) ) ) @ ( F @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__lex__prod_0) ).

thf(818,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ tc_prod ) @ ( F @ ( C @ tc_prod ) @ tc_prod ) @ ( F @ ( C @ ( H @ ( D @ c_Wellfounded_Olex__prod ) ) ) @ ( F @ ( C @ tc_prod ) @ ( F @ ( C @ tc_prod ) @ ( F @ ( C @ ( G @ ( B @ c_Pair ) ) ) @ ( F @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(289,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OBinOpRed1_0) ).

thf(1148,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(120,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OCond ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OCondThrow_0) ).

thf(735,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OCond ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(15,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I47_J_0) ).

thf(422,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(138,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I182_J_0) ).

thf(790,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(64,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OBinOp ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OBinOpThrow1_0) ).

thf(564,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OBinOp ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(144,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I166_J_0) ).

thf(807,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(179,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I4_J_0) ).

thf(897,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(248,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_TryReds_0) ).

thf(1056,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(85,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I153_J_0) ).

thf(635,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(105,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( I @ c_Expr_Oexp_OVal ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( H @ ( D @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OBinOp ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OBinOpThrow2_0) ).

thf(696,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( I @ c_Expr_Oexp_OVal ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( H @ ( D @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OBinOp ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(377,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( F @ ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_7) ).

thf(1346,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( F @ ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(174,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OSeqThrow_0) ).

thf(886,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(188,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( G @ ( F @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( D @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( C @ c_Map_Omap__add ) ) ) @ ( F @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ c_Map_Omap__add ) ) ) @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__lcl__add_0) ).

thf(918,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( G @ ( F @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( D @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( C @ c_Map_Omap__add ) ) ) @ ( F @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ c_Map_Omap__add ) ) ) @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(142,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I76_J_0) ).

thf(801,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(20,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( C @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I91_J_0) ).

thf(437,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( C @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(371,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( F @ c_Map_Omap__le ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__env__mono_0) ).

thf(1335,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( F @ c_Map_Omap__le ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(239,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I9_J_0) ).

thf(1033,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(309,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( D @ ( F @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_WellType_Osko__WellType__XWT__elim__cases__7__1 ) ) ) ) ) @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I7_J_1) ).

thf(1197,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( D @ ( F @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_WellType_Osko__WellType__XWT__elim__cases__7__1 ) ) ) ) ) @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(281,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).

thf(1129,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(336,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( G @ tc_prod ) @ ( C @ ( G @ tc_prod ) @ tc_prod ) @ ( C @ ( G @ ( D @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( G @ tc_prod ) @ ( C @ ( G @ tc_prod ) @ ( C @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ ( C @ ( G @ ( A @ ( E @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( G @ ( G @ tc_prod ) @ ( H @ ( G @ ( G @ ( F @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__lex__prod_1) ).

thf(1261,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( G @ tc_prod ) @ ( C @ ( G @ tc_prod ) @ tc_prod ) @ ( C @ ( G @ ( D @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( G @ tc_prod ) @ ( C @ ( G @ tc_prod ) @ ( C @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ ( C @ ( G @ ( A @ ( E @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( G @ ( G @ tc_prod ) @ ( H @ ( G @ ( G @ ( F @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(163,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCondThrow_0) ).

thf(860,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(52,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I147_J_0) ).

thf(528,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(382,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__Xhyps__2__1 ) ) ) ) @ ( v_e_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssRed1_Ohyps_I2_J_0) ).

thf(1357,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__Xhyps__2__1 ) ) ) ) @ ( v_e_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(184,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I55_J_0) ).

thf(908,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(115,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = H )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_2) ).

thf(723,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = H )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(354,axiom,
    tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( v_E____ @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf_0) ).

thf(1299,plain,
    tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( v_E____ @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(167,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DomainI_0) ).

thf(871,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(277,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Relation_OId__on ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).

thf(1120,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Relation_OId__on ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(267,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I138_J_0) ).

thf(1093,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(82,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I108_J_0) ).

thf(624,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(156,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I155_J_0) ).

thf(839,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(116,axiom,
    tc_bool @ class_HOL_Oord,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(728,plain,
    tc_bool @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(122,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
      = ( E @ ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__add ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__assoc_0) ).

thf(740,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
      = ( E @ ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__add ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(325,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Relation_OId__on ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).

thf(1236,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Relation_OId__on ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(218,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__iff_1) ).

thf(987,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(196,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).

thf(935,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(57,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I163_J_0) ).

thf(543,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(242,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I18_J_0) ).

thf(1037,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(99,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I193_J_0) ).

thf(676,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(39,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I81_J_0) ).

thf(491,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(172,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).

thf(882,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(232,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssReds2_0) ).

thf(1014,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( H @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(1367,plain,
    $false,
    inference(e,[status(thm)],[1036,1337,1168,846,893,1315,468,941,1179,479,1105,777,555,666,1295,1200,523,1005,730,1068,1269,861,873,1205,878,440,655,511,385,384,500,715,1275,1233,1327,747,945,1354,1222,1260,698,404,1196,417,973,1359,1265,1228,651,1243,1127,1287,1330,1323,1191,1132,1313,1279,902,1087,1247,1319,448,1100,638,853,924,591,443,514,937,966,1302,756,485,834,1020,574,1183,1283,1051,821,602,1072,396,1351,998,1345,428,920,942,1306,1199,1153,810,546,793,1311,534,798,1163,1223,1091,1343,952,1255,1123,1217,561,815,729,1238,407,693,916,566,682,842,1012,583,830,1159,461,1079,1027,1291,710,742,948,1064,980,1096,1006,388,869,783,989,1089,1234,471,884,1082,488,933,753,537,669,1016,1155,1075,476,679,1039,701,1297,1231,1131,1060,721,569,605,1263,997,515,1150,1249,984,911,1333,1086,508,1054,1170,558,926,398,1035,718,888,412,750,425,1146,824,745,732,1125,772,577,904,975,572,713,1058,466,804,704,947,540,672,391,1139,611,787,764,900,1117,1011,1349,1144,737,616,599,1175,880,434,890,1339,552,594,621,1325,895,769,1022,1177,494,1080,848,520,685,983,959,1066,780,455,608,1113,1000,1250,1102,505,431,653,922,658,1213,827,1044,1245,394,986,473,1304,1166,1208,531,795,663,1277,939,1018,836,1049,1134,648,968,458,1181,525,1003,690,640,1070,954,1267,409,1098,993,580,855,1225,707,414,971,673,1300,1186,463,1317,1285,643,1220,907,1257,1141,864,1008,446,1272,991,497,876,627,931,482,759,1216,1189,1108,450,1084,1157,1321,1289,844,517,1341,1062,632,401,786,995,588,1253,961,813,1030,914,1294,929,1077,832,1309,549,1161,1116,1348,1280,950,818,1148,735,422,790,564,807,897,1056,635,696,1346,886,918,801,437,1335,1033,1197,1129,1261,860,528,1357,908,723,1299,871,1120,1093,624,839,728,740,1236,987,935,543,1037,676,491,882,1014]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV954-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41  % Computer : n006.cluster.edu
% 0.14/0.41  % Model    : x86_64 x86_64
% 0.14/0.41  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41  % Memory   : 8046.5625MB
% 0.14/0.41  % OS       : Linux 6.8.0-71-generic
% 0.14/0.41  % CPULimit : 300
% 0.14/0.41  % WCLimit  : 300
% 0.14/0.41  % DateTime : Sat Sep 26 15:13:41 UTC 2026
% 0.14/0.42  % CPUTime  : 
% 0.14/0.42  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.81/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.24/1.43  % [INFO] 	 Parsing done (441ms). 
% 2.24/1.45  % [INFO] 	 Running in sequential loop mode. 
% 3.40/1.83  % [INFO] 	 eprover registered as external prover. 
% 3.40/1.84  % [INFO] 	 Scanning for conjecture ... 
% 4.20/2.08  % [INFO] 	 Found a conjecture (or negated_conjecture) and 396 axioms. Running axiom selection ... 
% 4.88/2.27  % [INFO] 	 Axiom selection finished. Selected 381 axioms (removed 15 axioms). 
% 6.31/2.54  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 6.31/2.56  % [INFO] 	 Type checking passed. 
% 6.31/2.56  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 18.60/5.51  % External prover 'e' found a proof!
% 18.60/5.51  % [INFO] 	 Killing All external provers ... 
% 18.60/5.51  % Time passed: 4954ms (effective reasoning time: 4058ms)
% 18.60/5.52  % Axioms used in derivation (381): clsarity_nat__HOL_Oord, cls_WTrt__elim__cases_I8_J_3, cls_WTFAcc_0, cls_exp_Osimps_I56_J_0, cls_exp_Osimps_I156_J_0, cls_exp_Osimps_I9_J_1, cls_WTSeq_0, cls_CallObjThrow_0, cls_red__reds_OLAssThrow_0, cls_WTrt__elim__cases_I8_J_9, cls_IH_0, cls_red__lcl__add_0, cls_rtrancl__idemp_0, cls_exp_Osimps_I92_J_0, cls_exp_Osimps_I195_J_0, cls_exp_Osimps_I103_J_0, cls_red__reds_OFAssRed2_0, cls_total__on__def_0, cls_equalityI_0, cls_exp_Osimps_I218_J_0, cls_exp_Osimps_I213_J_0, cls_CallRedsThrowObj_0, cls_FAssRed1_I2_J_1, cls_red__reds_OFAssRed1_0, cls_eval__cases_I1_J_1, cls_map__add__assoc_0, cls_exp_Osimps_I225_J_0, cls_eval__evals_OFAssThrow2_0, cls_exp_Osimps_I7_J_2, cls_map__le__trans_0, cls_le__funD_0, cls_exp_Osimps_I193_J_0, cls_CastReds_0, cls_exp_Osimps_I138_J_0, cls_exp_Osimps_I81_J_0, cls_exp_Osimps_I137_J_0, cls_BinOpRedsThrow2_0, cls_CallRedsObj_0, cls_BinOpRedsThrow1_0, cls_exp_Osimps_I219_J_0, cls_extend__eval_0, cls_has__visible__field_0, cls_lconf__hext_0, cls_WT__elim__cases_I8_J_0, cls_exp_Osimps_I11_J_0, cls_CHAINED_0, cls_Id__on__eqI_0, cls_eval__evals_OCondThrow_0, cls_WTrt__elim__cases_I8_J_14, cls_exp_Osimps_I15_J_1, cls_ty_Osimps_I8_J_0, cls_exp_Osimps_I211_J_0, cls_rtrancl__trans_0, cls_BinOp2Reds_0, clsarity_nat__Orderings_Olinorder, cls_widen__Class_2, cls_exp_Osimps_I115_J_0, cls_map__le__iff__map__add__commute_0, cls_mem__def_1, cls_FAssReds2_0, cls_WT__elim__cases_I7_J_1, cls_exp_Osimps_I154_J_0, cls_WTrt__elim__cases_I6_J_0, cls_COMBI__def__raw_0, cls_SeqReds2_0, cls_ty_Osimps_I20_J_0, cls_exp_Osimps_I141_J_0, cls_WT__elim__cases_I8_J_4, cls_WTrt__elim__cases_I8_J_10, cls_exp_Osimps_I97_J_0, cls_exp_Osimps_I170_J_0, cls_LAssReds_0, cls_WTrt_H__elim__cases_0, cls_red__reds_OFAssThrow2_0, cls_exp_Osimps_I188_J_0, cls_set__rev__mp_0, cls_exp_Osimps_I109_J_0, cls_WTrt__elim__cases_I8_J_7, cls_exp_Osimps_I212_J_0, cls_red_0, cls_Range__Id__on_0, cls_refl__on__Id__on_0, cls_exp_Osimps_I8_J_3, cls_in__lex__prod_1, cls_WTrt__elim__cases_I8_J_2, cls_exp_Osimps_I2_J_1, cls_exp_Osimps_I79_J_0, cls_exp_Osimps_I206_J_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_exp_Osimps_I194_J_0, cls_exp_Osimps_I113_J_0, cls_exp_Osimps_I11_J_1, cls_WTThrow_0, cls_map__le__implies__dom__le_0, cls_exp_Osimps_I171_J_0, cls_red__reds_OCallThrowObj_0, cls_red__reds_OLAssRed_0, cls_exp_Osimps_I157_J_0, cls_exp_Osimps_I136_J_0, cls_exp_Osimps_I175_J_0, cls_exp_Osimps_I4_J_1, cls_WTrt_H__WTrts_H_Ointros_I9_J_0, cls_eval__evals_OSeqThrow_0, cls_exp_Osimps_I67_J_0, cls_converse__rtrancl__into__rtrancl_0, cls_exp_Osimps_I4_J_0, cls_hext__trans_0, cls_exp_Osimps_I160_J_0, cls_exp_Osimps_I84_J_0, cls_widen__refl_0, cls_CondReds_0, cls_WTrt__elim__cases_I8_J_6, cls_WT__elim__cases_I4_J_0, cls_map__le__def_0, cls_hext__refl_0, cls_SigmaI_0, cls_exp_Osimps_I74_J_0, cls_red__reds_OThrowThrow_0, cls_red__reds_OCallObj_0, cls_exp_Osimps_I9_J_0, cls_exp_Osimps_I85_J_0, cls_eval__evals_OBinOpThrow2_0, cls_eval__evals_OFAccThrow_0, cls_exp_Osimps_I176_J_0, cls_widen_Ocases_0, cls_refl__on__def_1, cls_exp_Osimps_I146_J_0, cls_exp_Osimps_I174_J_0, cls_ty_Osimps_I9_J_0, cls_map__add__dom__app__simps_I2_J_0, cls_red__reds_OBinOpThrow1_0, cls_WTrtFAssNT_0, cls_exp_Osimps_I139_J_0, cls_void_0, cls_ThrowReds_0, cls_conf_0, cls_subset__iff_0, cls_exp_Osimps_I46_J_0, cls_map__le__refl_0, clsarity_fun__HOL_Oord, cls_exp_Osimps_I99_J_0, cls_WTrtFAccNT_0, cls_WTrt__hext__mono_0, cls_WTrtFAss_0, cls_eval__evals_OFAssThrow1_0, cls_rev__predicate1D_0, cls_WTFAss_0, cls_WTrt_H__WTrts_H_Ointros_I11_J_0, cls_acc__downwards__aux_0, cls_red__reds_OTryRed_0, cls_WT__elim__cases_I8_J_3, cls_in__lex__prod_2, cls_WTrt__elim__cases_I8_J_13, cls_WTrt__env__mono_0, cls_exp_Osimps_I180_J_0, cls_WT__elim__cases_I6_J_0, cls_red__preserves__sconf_0, cls_FAccReds_0, cls_exp_Osimps_I77_J_0, cls_map__add__dom__app__simps_I3_J_0, cls_Range__iff_1, cls_exp_Osimps_I69_J_0, cls_exp_Osimps_I98_J_0, cls_exp_Osimps_I61_J_0, cls_exp_Osimps_I15_J_0, cls_exp_Osimps_I183_J_0, cls_exp_Osimps_I2_J_0, cls_Id__on__iff_0, cls_exp_Osimps_I12_J_2, cls_exp_Osimps_I8_J_2, cls_SigmaD2_0, cls_set__eq__subset_2, cls_Seq_0, cls_exp_Osimps_I207_J_0, cls_calculation_0, cls_exp_Osimps_I76_J_0, cls_exp_Osimps_I70_J_0, cls_exp_Osimps_I177_J_0, cls_FAssRedsThrow2_0, cls_linorder__linear_0, cls_DomainI_0, cls_exp_Osimps_I62_J_0, cls_red__reds_OBinOpRed2_0, cls_TryReds_0, cls_exp_Osimps_I186_J_0, cls_exp_Osimps_I210_J_0, cls_ty_Osimps_I7_J_0, cls_acc__downwards_0, cls_exp_Osimps_I112_J_0, cls_exp_Osimps_I60_J_0, cls_exp_Osimps_I162_J_0, cls_CondRedsThrow_0, cls_subset__trans_0, cls_refl__onD2_0, cls_map__add__le__mapE_0, cls_acc_Ocases_0, cls_exp_Osimps_I15_J_3, cls_exp_Osimps_I169_J_0, cls_SigmaD1_0, cls_exp_Osimps_I166_J_0, cls_mem__def_0, cls_red__reds_OFAssThrow1_0, cls_Image__iff_2, cls_TryRedsVal_0, cls_exp_Osimps_I47_J_0, cls_exp_Osimps_I7_J_1, cls_WTrtSeq_0, cls_exp_Osimps_I189_J_0, cls_WTrt__elim__cases_I8_J_5, cls_exp_Osimps_I224_J_0, cls_eval__evals_OThrowThrow_0, cls_red__reds_OBinOpRed1_0, cls_rtrancl__eq__or__trancl_1, cls_exp_Osimps_I55_J_0, cls_exp_Osimps_I101_J_0, cls_exp_Osimps_I102_J_0, cls_CastRedsThrow_0, cls_exp_Osimps_I75_J_0, cls_SeqRedsThrow_0, cls_red__reds_OSeqRed_0, cls_WT__elim__cases_I1_J_0, cls_exp_Osimps_I80_J_0, cls_refl__onD_0, cls_subset__refl_0, cls_exp_Osimps_I145_J_0, cls_Pair__eq_0, cls_in__lex__prod_3, cls_rev__ImageI_0, cls_exp_Osimps_I182_J_0, cls_wt_0, cls_ty_Oinject_0, cls_exp_Osimps_I68_J_0, cls_map__le__antisym_0, cls_WT__implies__WTrt_0, cls_LAssRedsThrow_0, cls_exp_Osimps_I4_J_2, cls_exp_Osimps_I114_J_0, cls_evals__hext_0, cls_exp_Osimps_I216_J_0, cls_FAssRed1_Ohyps_I2_J_0, cls_red__reds_OCastThrow_0, cls_WTrt_H__WTrts_H_Ointros_I18_J_0, cls_extend__1__eval_0, cls_exp_Osimps_I57_J_0, cls_FAssRed1_Ohyps_I2_J_1, cls_eval__evals_OCastThrow_0, cls_exp_Osimps_I93_J_0, cls_WTrt_H__WTrts_H_Ointros_I8_J_0, cls_SeqReds_0, cls_exp_Osimps_I53_J_0, cls_exp_Osimps_I152_J_0, cls_eval__evals_OLAssThrow_0, cls_exp_Osimps_I50_J_0, cls_red__reds_OThrowRed_0, cls_Domain__Id__on_0, cls_WTrtFAcc_0, cls_widen__Class_0, cls_red__reds_OFAccRed_0, cls_exp_Osimps_I54_J_0, cls_exp_Osimps_I86_J_0, cls_refl__onD1_0, cls_exp_Osimps_I8_J_1, cls_exp_Osimps_I144_J_0, cls_exp_Osimps_I150_J_0, cls_Not__Domain__rtrancl_0, cls_exp_Osimps_I106_J_0, cls_wt_H__wt_0, cls_equiv_Orefl__on_0, cls_exp_Osimps_I66_J_0, cls_subsetD_0, cls_exp_Osimps_I6_J_0, cls_exp_Osimps_I108_J_0, cls_red__reds_OBinOpThrow2_0, cls_WT__elim__cases_I8_J_2, cls_WTrt__elim__cases_I8_J_12, cls_exp_Osimps_I90_J_0, cls_ty_Osimps_I21_J_0, cls_FAccRedsThrow_0, cls_widen__trans_0, cls_WTrt__elim__cases_I7_J_1, cls_ty_Osimps_I6_J_0, cls_exp_Osimps_I155_J_0, cls_RangeI_0, cls_eval__cases_I1_J_0, cls_red__reds_OCondThrow_0, cls_exp_Osimps_I12_J_1, cls_FAssRedsThrow1_0, cls_red__preserves__hconf_0, cls_rtrancl_Ortrancl__refl_0, cls_exp_Osimps_I71_J_0, cls_Id__on__iff_1, cls_eval__evals_OBinOpThrow1_0, cls_sees__field__fun_1, cls_WT__elim__cases_I5_J_0, cls_equiv__class__eq__iff_1, cls_exp_Osimps_I14_J_0, cls_exp_Osimps_I107_J_0, cls_exp_Osimps_I167_J_0, cls_exp_Osimps_I9_J_2, cls_exp_Osimps_I161_J_0, cls_exp_Osimps_I7_J_0, cls_exp_Osimps_I217_J_0, cls_exp_Osimps_I45_J_0, cls_red__lcl__incr_0, cls_exp_Osimps_I8_J_0, cls_exp_Osimps_I44_J_0, cls_ThrowRedsThrow_0, cls_exp_Osimps_I192_J_0, cls_exp_Osimps_I151_J_0, cls_same__fstI_0, cls_map__add__dom__app__simps_I1_J_0, cls_exp_Osimps_I153_J_0, cls_WTrt__elim__cases_I8_J_4, cls_eval__lcl__incr_0, cls_rtrancl_Ortrancl__into__rtrancl_0, cls_exp_Osimps_I6_J_1, cls_red__reds_OSeqThrow_0, cls_Try_0, cls_exp_Osimps_I51_J_0, cls_WTrt__elim__cases_I1_J_0, cls_BinOp1Reds_0, cls_red__hext__incr_0, cls_exp_Osimps_I52_J_0, cls_red__reds_OCastRed_0, cls_WTrt__elim__cases_I8_J_0, cls_Val_0, cls_FAssReds1_0, cls_acc__downward_0, cls_exp_Osimps_I15_J_2, cls_r__into__rtrancl_0, cls_red__reds_OFAccThrow_0, cls_wt__env__mono_0, cls_mem__Sigma__iff_2, cls_exp_Osimps_I187_J_0, cls_sees__field__idemp_0, cls_eval__hext_0, cls_exp_Osimps_I96_J_0, cls_wt__wt_H_0, cls_exp_Osimps_I91_J_0, cls_exp_Osimps_I181_J_0, cls_WT__elim__cases_I7_J_0, cls_exp_Osimps_I168_J_0, cls_sees__field__fun_0, cls_exp_Osimps_I63_J_0, cls_that_0, cls_Domain__iff_1, cls_Not__Domain__rtrancl_1, cls_exp_Osimps_I140_J_0, cls_COMBI__def_0, cls_red__preserves__lconf_0, cls_red__reds_OCondRed_0, cls_map__le__iff__map__add__commute_1, cls_map__le__map__add_0, cls_WTrt__elim__cases_I8_J_11, cls_Red__lcl__add_0, cls_exp_Osimps_I87_J_0, cls_exp_Osimps_I78_J_0, cls_equiv__class__eq__iff_2, cls_exp_Osimps_I12_J_0, cls_Pair__eq_1, cls_big__by__small_0, cls_WTrt__elim__cases_I7_J_0, cls_FAssRed1_I2_J_0, cls_exp_Osimps_I100_J_0, cls_equalityE_0, cls_exp_Osimps_I163_J_0, cls_red__reds_ORedSeq_0, cls_map__add__le__mapI_0, cls_widen_Ocases_2, cls_in__lex__prod_0, cls_exp_Osimps_I147_J_0, cls_WTrt_H__WTrts_H_Ointros_I10_J_0, cls_exp_Osimps_I3_J_0, cls_red__reds_ORedTry_0, cls_WTrt__elim__cases_I8_J_8, cls_predicate1D_0, cls_evals__lcl__incr_0, cls_IH_1, cls_WTrt__elim__cases_I8_J_1, cls_WT__elim__cases_I8_J_1
% 18.60/5.52  % No. of inferences in proof: 767
% 18.60/5.52  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4954 ms resp. 4058 ms w/o parsing
% 20.86/6.14  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.20/6.15  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------